Nonlinear analysis of the forced response of a beam with three mode interaction

An analysis is presented for the primary resonance of a clamped-hinged beam, which occurs when the frequency of excitation is near one of the natural frequencies,_n . Three mode interaction (₂ 3₁ and _{3 1} + 2₂) is considered and its influence on the response is studied. The case of two mode interaction (₂ 3₁) is also considered to compare it with the case of three mode interaction. The straight beam experiencing mid-plane stretching is governed by a nonlinear partial differential equation. By using Galerkin's method the governing equation is reduced to a system of nonautonomous ordinary differential equations. The method of multiple scales is applied to solve the system. Steady-state responses and their stability are examined. Results of numerical investigations show that there exists no significant difference between both modal interactions' influences on the responses.     

Improvements on open and traction boundary conditions for Navier–Stokes time-splitting methods

We present in this paper a numerical scheme for incompressible Navier–Stokes equations with open and traction boundary conditions, in the framework of pressure-correction methods. A new way to enforce this type of boundary condition is proposed and provides higher pressure and velocity convergence rates in space and time than found in the present state of the art. We illustrate this result by computing some numerical and physical tests. In particular, we establish reference solutions of a laminar flow in a geometry where a bifurcation takes place and of the unsteady flow around a square cylinder.     

Electrogravitational stability of oscillating streaming fluid cylinder

The electrogravitational instability of on oscillating streaming fluid cylinder under the action of the selfgravitating, capillary and electrodynamic forces has been discussed. The model is governed by the Mathieu second order integro-differential equation. Some limiting cases are recovering from the present general one. The capillary force is destabilizing in a small axisymmetric domain 0<x<1 and stabilizing otherwise. In the absence of electric fields, we found that the model is unstable in a small domain while it is selfgravitating stable in all other domains. The presence of the electric field led to the presence of a great number of stable waves. The electric field has a strong stabilizing influence on the selfgravitating instability of the model. The capillary force has a strong destabilizing influence on the selfgravitating instability of the model.Generally, the uniform stream supports the unstable waves, while the oscillating streaming has stability tendency.     

Correlation between helical surface waves and guided modes of an infinite immersed elastic cylinder

Scattering of obliquely incident plane acoustic waves from immersed infinite solid elastic cylinders is a complex phenomenon that involves generation of various types of surface waves on the body of the cylinder. Mitri [F.G. Mitri, Acoustic backscattering enhancement resulting from the interaction of an obliquely incident plane wave with an infinite cylinder, Ultrasonics 50 (2010) 675-682] recently showed that for a solid aluminum cylinder, there exist acoustic backscattering enhancements at a normalized frequency of ka?0.1. The incidence angle α_c at which these enhancements are observed lies between the first (longitudinal) and second (shear) coupling angles of the cylinder. He also confirmed the observations previously reported by the authors that there exist backscattering enhancements of the dipole mode at large angles of incidence where no wave penetration into the cylinder is expected. In this paper, physical explanations are provided for the aforementioned observations by establishing a correlation between helical surface waves generated by oblique insonification of an immersed infinite solid elastic cylinder and the longitudinal and flexural guided modes that can propagate along the cylinder. In particular, it is shown that the backscattering enhancement observed at ka?0.1 is due to the excitation of the first longitudinal guided mode travelling at the bar velocity along the cylinder. It is also demonstrated that the dipole resonance mode observed at incidence angles larger than the Rayleigh coupling angle is associated with the first flexural guided mode of the cylinder. The correlation established between the scattering and propagation problems can be used in both numerical and experimental studies of interaction of mechanical waves with cylinders.     

Zonal flow induced by longitudinal librations of a rotating cylindrical cavity

Longitudinal librations represent oscillations about the axis of a rotating axisymmetric fluid filled cavity. An analytical theory is developed for the case of a cylindrical cavity in the limit when the libration frequency is small in comparison with the rotation rate, but large in comparison with the inverse of the spin-up time. It is shown that through the nonlinear advection in the Ekman layers the librations cause the fluid to rotate more slowly.     

掠过双板流动引起的旋涡脱落特性数值模拟

板状燃料组件在先进核反应堆中得到重要应用.流体以一定的流速轴掠板状组件时会导致板后产生旋涡脱落现象.旋涡脱落有可能引发板状燃料组件的流致振动.使用BELIEF程序,通过改变方柱间距模拟了Re=200情况下刚性矩形通道内不同节距条件下双平行方柱的旋涡脱落现象,得出了双柱间节距对双平行方柱旋涡脱落特性的影响,并进一步对双平...     

Ultrasound velocimetry of ferrofluid spin-up flow measurements using a spherical coil assembly to impose a uniform rotating magnetic field

Ferrofluid spin-up flow is studied within a sphere subjected to a uniform rotating magnetic field from two surrounding spherical coils carrying sinusoidally varying currents at right angles and 90° phase difference. Ultrasound velocimetry measurements in a full sphere of ferrofluid shows no measureable flow. There is significant bulk flow in a partially filled sphere (1-14 mm/s) of ferrofluid or a finite height cylinder of ferrofluid with no cover (1-4 mm/s) placed in the spherical coil apparatus. The flow is due to free surface effects and the non-uniform magnetic field associated with the shape demagnetizing effects. Flow is also observed in the fully filled ferrofluid sphere (1-20 mm/s) when the field is made non-uniform by adding a permanent magnet or a DC or AC excited small solenoidal coil. This confirms that a non-uniform magnetic field or a non-uniform distribution of magnetization due to a non-uniform magnetic field are causes of spin-up flow in ferrofluids with no free surface, while tangential magnetic surface stress contributes to flow in the presence of a free surface.Recent work has fitted velocity flow measurements of ferrofluid filled finite height cylinders with no free surface, subjected to uniform rotating magnetic fields, neglecting the container shape effects which cause non-uniform demagnetizing fields, and resulting in much larger non-physical effective values of spin viscosity η′∼10⁻⁸−10⁻¹² N s than those obtained from theoretical spin diffusion analysis where η′≤10⁻¹⁸ N s. COMSOL Multiphysics finite element computer simulations of spherical geometry in a uniform rotating magnetic field using non-physically large experimental fit values of spin viscosity η′∼10⁻⁸−10⁻¹² N s with a zero spin-velocity boundary condition at the outer wall predicts measureable flow, while simulations setting spin viscosity to zero (η′=0) results in negligible flow, in agreement with the ultrasound velocimetry measurements. COMSOL simulations also confirm that a non-uniform rotating magnetic field or a uniform rotating magnetic field with a non-uniform distribution of magnetization due to an external magnet or a current carrying coil can drive a measureable flow in an infinitely long ferrofluid cylinder with zero spin viscosity (η′=0).     

Effect of biaxial orientation on dielectric and breakdown properties of poly(ethylene terephthalate)/poly(vinylidene fluoride‐co‐tetrafluoroethylene) multilayer films

Polymer films with enhanced dielectric and breakdown properties are essential for the production of high energy density polymer film capacitors. By capitalizing on the synergistic effects of forced assembly nanolayer coextrusion and biaxial orientation, polymer multilayer films using poly(ethylene terephthalate) (PET) and a poly(vinylidene fluoride‐co‐tetrafluoroethylene) [P(VDF‐TFE)] copolymer were produced. These films exhibited breakdown fields, under a divergent field using needle/plane electrodes, as high as 1000 kV mm^?1. The energy densities of these same materials, under a uniform electric field measured using plane/plane electrodes, were as high as 16 J cm^?3. The confined morphologies of both PET and P(VDF‐TFE) were correlated to the observed breakdown properties and damage zones. On‐edge P(VDF‐TFE) crystals induced from solid‐state biaxial stretching enhanced the effective P(VDF‐TFE) layer dielectric constant and therefore increased the dielectric contrast between the PET and P(VDF‐TFE) layers. This resulted in additional charge buildup at the layer interface producing larger tree diameters and branches and ultimately increasing the breakdown and energy storage properties. In addition to energy storage and breakdown properties, the hysteresis behavior of these materials was also evaluated. By varying the morphology of the P(VDF‐TFE) layer, the low‐field dielectric loss (or ion migration behavior) could be manipulated, which in turn also changed the observed hysteresis behavior. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2013, 51, 882–896     

MHD flow and heat transfer over permeable stretching sheet with slip conditions

The magnetohydrodynamic (MHD) flow and heat transfer characteristics for the boundary layer flow over a permeable stretching sheet are considered. Velocity and thermal slip conditions are taken into account. Problem formulation is developed in the presence of thermal radiation. Governing non‐linear problem is solved by a homotopy analysis method. Convergence of the derived solutions is studied. Numerical values of skin‐friction coefficient and local Nusselt number are tabulated. Effects of pertinent parameters on the velocity and temperature profiles are discussed. Comparison between the present and previous limiting results is shown. Copyright © 2010 John Wiley & Sons, Ltd.     

旋转液体中固体颗粒运动的进一步讨论

通过分析旋转液体中的压强分布,说明了浸在液体中的固体颗粒向轴心运动的原因,以及该规律的实际应用.